Concentration fluctuations in adsorbed layers

The temperature and coverage dependence of the mean square concentration fluctuations in a small open domain of an adsorbed layer is discussed for various situations. It is shown that fluctuations decrease with increasing temperature and reach a limiting value when attractive interactions predominate, but increase and reach a limiting value when repulsive interactions predominate, if a single non-ideal two -dimensional phase exists. Deviations from ideal gas behavior are strongest at half coverage. At very low coverage (low particle concentration) and very high coverage (low hole concentration) ideal behavior is approached. If the layer consists of a two phase system, for instance a two-dimensional liquid or solid in equilibrium with a two-dimensional gas, fluctuations far below the critical temperature are dominated by fluctuations in the partition between phases. As the critical temperature is approached fluctuations first decrease because the mean concentrations in the two phases approach each other, and then increase very sharply near T_c. Detailed calculations for the single phase situation are given for several approximations: a dilute gas; a mean field approximation; a lattice gas in both the Bragg-Williams and the BethePeierls-Weiss approximations. The latter which takes some account of correlations between adsorbate particle positions seems to explain reasonably the presently available experimental observations on chemisorbed layers.     

Adsorption of interacting monomers on spanning clusters of polyatomic species

The adsorption-desorption process occurring on heterogeneous surfaces is studied by considering a special case where a fractal is used as adsorbent. The fractal surface is the spanning cluster corresponding to the random deposition of objects that occupy more than one site (k-mers) on a square lattice. Such a surface is characterized according to the deposited k-mer. Then, the adsorption of repulsively interacting particles adsorbed on the fractal surface is studied by using Monte Carlo simulations. Different thermodynamic quantities (adsorption isotherms, coverage susceptibility, etc.) are calculated and explained in terms of the characteristics of the substrate. A scheme to characterize the structure of the substrate by just considering the adsorption isotherm is presented and discussed.     

Phase behaviors of strongly correlated Fermi gases in one-dimensional confinements

We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k _F → 4k _F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.     

On the calculation of the classical Liouville operator for the step-type interparticle interaction

A new method of the determination of the Liouville operator for the step-type interparticle interaction is presented. The interaction part of the Liouville operator is calculated for the particles interacting via a spherical repulsive and spherical attractive barrier. Limiting cases of an infinitely high (hard core) and infinitely deep barrier are discussed. These results can be used for the determination of the interaction part of the Liouville operator for an arbitrary step-type interaction which can be expressed as a sum of several attractive and repulsive barriers.     

Critical behavior of long linear k-mers on honeycomb lattices

Monte Carlo (MC) simulations, finite-size scaling and theoretical analysis have been carried out to study the critical behavior of long linear particles of length k (k-mers) on honeycomb lattices. A nematic phase, characterized by a big domain of parallel k-mers, is separated from the isotropic state, by a continuous transition occurring at a finite density θ_c. Our study allowed: (1) to determine the minimum value of k (k_min), which allows the formation of the nematic phase, being k_min=11; (2) to predict the dependence of θ_c on k, being θ_c(k)∝k⁻¹; and (3) to obtain the critical exponents, which indicate that the transition belongs to the 2D three-state Potts universality class.     

Diffusion of spheres in a concentrated suspension II

We evaluate the wavevector dependent (short-time) diffusion coefficient D(k) for spherical particles in suspension, by extending a previous study of selfdiffusion (which corresponds to the case of large k). Our analysis is valid up to high concentrations and fully takes into account the many-body hydrodynamic interactions between an arbitrary number of spheres, as well as the resummed contributions from a special class of correlations. Results obtained which agree well with available experimental data.     

Adsorption thermodynamics of interacting particles on diffusion-limited aggregates

Grand canonical Monte Carlo simulations have been performed in order to study adsorption thermodynamics of pairwise interacting particles on fractal surfaces. Diffusion-limited aggregates (DLA) have been used as a substrate where interacting particles are adsorbed. In order to obtain aggregates with different morphologies, DLA clusters are generated on different strongly correlated surfaces. Adsorption isotherm, adsorption energy and differential heat of adsorption were calculated for attractive and repulsive nearest-neighbor (NN) lateral interactions. For the case of repulsive couplings and low temperatures, four novel ordered phases has been found in the adsorbate, each one corresponding to the formation of a chessboard-like structure on sites with one, two, three and four NN sites, respectively. The values of coverage at which these ordered phases emerge are not symmetrical around θ=0.5. This is a consequence of the non-equivalence between vacancy and particle in the case of adsorption on fractal structures. The influence of ordered structures on thermodynamic quantities associated to the adsorbed monolayer has been analyzed and discussed in the context of the Lattice-Gas model.     

Modeling of electron-stimulated mobility and disordering of adsorbed particles

The electron-stimulated mobility and the electron-stimulated disordering of adsorbed particles is studied for a two-dimensional lattice gas model on a square lattice using kinetical Monte Carlo simulations. Pairwise nearest-neighbor repulsive interactions are considered which induce c(2 × 2) ordering of the lattice gas at low temperatures around half coverage. Adsorbed particles are allowed to perform thermally activated as well as electron-induced jumps to nearest-neighbor sites. The calculations are performed taking full advantage of the numerical power of a supermassive parallel computer.

It was found that the electron-induced mobility of adatoms causes the complete breakdown of the c(2 × 2) ordering at low temperatures if the fraction of electron-induced jumps exceeds a critical value. The breakdown of the ordering is accompanied by substantial changes of the chemical and tracer surface diffusion coefficients.     

Depletion potentials between colloids and patterned surfaces

Effective interactions between the hard-sphere colloids and the patterned substrates created by depositing one or more hemispheres on the structureless walls are studied. The deposition of only one hemispherical cap gives rise to a new global minimum of the depletion potential but the difference from the planar hard wall case is moderate. On the other hand, when the hemispherical caps form a periodic array, multiple overlaps of the excluded volumes lead to formation of deep global minimum of the depletion potential. In some cases this minimum is deeper than −10k_BT and this is more than triple of the potential minimum for the structureless wall. We conclude that templated surfaces affect depletion potentials significantly. This effect will have a major impact even when the residual attractive/repulsive interactions are present.     

Study of static and thermophysical properties of alkaline earth fluoride crystals

An analysis for cohesive energy, bulk modulus and its pressure derivatives in BaF₂, SrF₂ and CaF₂ crystals has been carried out by means of interionic potential model. Interionic potential consist of long range coulomb and three-body interactions along with short-range attractive van der Waals and repulsive Hafemeister-Zarht type interactions. The three body force parameter $\text{?(r)}$ and vdWI coefficients C and D are determined using the Cochran's formula and Slater-Kirkwood variational (SKV) integrals. The calculated values of cohesive energy, bulk modulus and its pressure derivatives for solids under study are found generally in good agreement with available experimental data. The results achieved by other investigations [13, 14] have also been compared with results calculated in the present study.     

Unified properties of a weakly interacting Fermi gas in a weak magnetic field

When the orbital motion and the spin motion of particles were considered simultaneously, the thermodynamic potential function of a weakly interacting Fermi gas in a weak magnetic field was derived using the thermodynamics method. Based on the derived expression, the analytical expressions of energy, heat capacity, chemical potential, susceptibility and stability conditions of the system were given, and the effects of the interparticle interactions as well as the magnetic field on the properties of the system were analyzed. It was shown that the magnetic field always causes energy and stability to decrease, while the chemical potential of the system to increase. The repulsive (attractive) interactions always increase (decrease) energy and stability, but decrease (increase) the chemical potential and paramagnetism. The repulsive (attractive) interactions decrease (increase) heat capacity of the system at high temperatures but increase (decrease) it at low temperatures.     

对利用动态光散射法测量颗粒粒径和液体黏度的改进

光散射技术通过测量悬浮液中布朗运动颗粒的平移扩散系数,得到颗粒流体力学直径或液体黏度.本文由单参数模型入手,建立了低颗粒浓度下,单颗粒平移扩散系数与颗粒集体平移扩散系数和颗粒浓度之间的线性依存关系并将其引入光散射法中,从而对现有的测量方法进行了改进.改进后的测量方法可实现纳米尺度球型颗粒标称直径的测量和液体黏度的绝对法测量.以聚苯乙烯颗粒+水和二氧化硅颗粒+乙醇两个分散系为参考样本,通过实验,验证了改进后方法的可行性.此外,还针对上述两个分散系,实验探讨了温度和颗粒浓度对颗粒集体平移扩散系数的影响规律,发现聚苯乙烯颗粒+水分散系中,颗粒间相互作用表现为引力;二氧化硅颗粒+乙醇分散系中,颗粒间相互作用表现为斥力.讨论了颗粒集体平移扩散系数随颗粒浓度变化规律与第二渗透维里系数的关系.     

A simulation study of the effects of adsorbent energy on the diffusion of molecules in slit pores: 1 commensurate slit widths

Equilibrium molecular dynamics simulation has been used to study the self-diffusion coefficients (from correlation of the molecular velocity) and the collective, or centre of mass diffusion coefficients (from correlation of the streaming velocity) of a Lennard-Jones fluid in model slit pores. The slit widths were chosen to be integer multiples of the Lennard-Jones adsorbate diameter, and therefore are close to being commensurate with layered adsorbate structures. Slits of reduced width H* = 3 and 5 were examined at a reduced temperature of T* = 1.0. The adsorbate densities ranged from 0.3 to 0.9 in reduced units. The adsorbent adsorbate interaction was modelled as a simple potential with inverse 4th power attraction plus hard wall repulsion, and systems with reduced parameter u₀* ranging from ?5 to +5 were studied. Molecule-wall scattering was represented by a diffuse reflection algorithm. The density distributions show strong layering in the attractive system, but this is absent in the most repulsive slits, except at very high densities. Self-diffusion is only weakly dependent on u₀* and slit width at high densities, but a strong dependence on u₀* appears at low densities. The collective diffusion coefficient is less easy to calculate with high accuracy; nevertheless, it is clear that there is a strong dependence of this property on u₀* Trajectory plots show zones in which the particles are more or less strongly localized, but undergo irregular oscillatory motion corresponding to regions of high density in the single-particle distributions.     

Order statistics for first passage times in diffusion processes

We consider the problem of the first passage times for absorption (trapping) of the firstj (j = 1,2, ....) ofk, j <k, identical and independent diffusing particles for the asymptotic case k?>1. Our results are a special case of the theory of order statistics. We show that in one dimension the mean time to absorption at a boundary for the first ofk diffusing particles, μ_1,k , goes as (lnk)^?1 for the set of initial conditions in which none of thek particles is located at a boundary and goes ask ^?2 for the set of initial conditions in which some of thek particles may be located at the boundary. We demonstrate that in one dimension our asymptotic results (k21) are independent of the potential field in which the diffusion takes place for a wide class of potentials. We conjecture that our results are independent of dimension and produce some evidence supporting this conjecture. We conclude with a discussion of the possible import of these results on diffusion-controlled rate processes.     

Percolation of polyatomic species on a simple cubic lattice

In the present paper, the site-percolation problem corresponding to linear k-mers (containing k identical units, each one occupying a lattice site) on a simple cubic lattice has been studied. The k-mers were irreversibly and isotropically deposited into the lattice. Then, the percolation threshold and critical exponents were obtained by numerical simulations and finite-size scaling theory. The results, obtained for k ranging from 1 to 100, revealed that (i) the percolation threshold exhibits a decreasing function when it is plotted as a function of the k-mer size; and (ii) the phase transition occurring in the system belongs to the standard 3D percolation universality class regardless of the value of k considered.     

Theoretical description of adatom migration in two-dimensional highly-ordered states

Analytical expressions for chemical, jump, and tracer diffusion coefficients are obtained for interacting lattice gases on a square lattice. Strongly repulsive nearest neighbor interactions cause the formation of a highly-ordered c() state in the vicinity of half coverage. It is shown that only strongly correlated successive adatom jumps contribute to the particle flow. This allows to describe the adatom kinetics by considering an almost ideal lattice gas of defects. Two types of defects are considered, adatoms in the empty sublattice and vacancies in the filled sublattice of the c() ordered state. The diffusion equations for these defects are developed considering the generation and recombination of defects. In addition we have considered adatom transport caused by the motion of defect pairs (dimers). Dimer transport mechanism prevails in the high coverage region. The characteristic features of the various diffusion coefficients near half coverage are analyzed and discussed. The theory is compared with the results of sophisticated Monte-Carlo simulations which have been executed with the use of a fully parallelized algorithm on a Cray T3E (LC784-128). The agreement between theoretical and MC results is excellent if the motion of dimers at is taken into account. Received 24 June 1998